The interaction and self-modulation of waves in periodic structures with random inhomogeneities

Theoretical and experimental results are presented on the interaction and self-modulation of quasi-monochromatic waves in a nonlinear periodic structure - a discrete LC line with random dispersion of capacitance. An asymptotic method is used to obtain equations in the first approximation for amplitudes of interacting waves in a line with quadratic nonlinearity as well as equations for the envelope of a wave packet undergoing self-modulation in a line with cubic nonlinearity. It is shown that interaction and self-modulation lead to damping of the mean wave field and deviation of the carrier frequency of the wave packet, associated with scattering of the wave field on random inhomogeneities.